Решите неравенство: x^2-4x+6>|x+2|.

\[x^{2} - 4x + 6 > |x + 2|\]

\[1.\ \ \left\{ \begin{matrix} x^{2} - 4x + 6 > x + 2 \\ x + 2 \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x^{2} - 5x + 4 > 0 \\ x \geq - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x² - 5x + 4 = 0\]

\[x_{1} + x_{2} = 5,\ \ x_{1} \cdot x_{2} = 4\]

\[x = 4,\ \ x = 1\]

\[\lbrack - 2;1) \cup (4;\ + \infty).\]

\[2.\ \ \left\{ \begin{matrix} x^{2} - 4x + 6 > - x - 2 \\ x + 2 < 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x^{2} - 3x + 8 > 0 \\ x < - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x² - 3x + 8 = 0\]

\[D = 9 - 32 < 0\]

\[( - \infty; - 2).\]

\[Ответ:( - \infty;1) \cup (4;\ + \infty).\]